Computer-Inspired Concept for High-Dimensional Multipartite Quantum Gates.

An open question in quantum optics is how to manipulate and control complex quantum states in an experimentally feasible way. Here we present concepts for transformations of high-dimensional multiphotonic quantum systems. The proposals rely on two new ideas: (i) a novel high-dimensional quantum nondemolition measurement, (ii) the encoding and decoding of the entire quantum transformation in an ancillary state for sharing the necessary quantum information between the involved parties. Many solutions can readily be performed in laboratories around the world and thereby we identify important pathways for experimental research in the near future. The concepts have been found using the computer algorithm melvin for designing computer-inspired quantum experiments. As opposed to the field of machine learning, here the human learns new scientific concepts by interpreting and analyzing the results presented by the machine. This demonstrates that computer algorithms can inspire new ideas in science, which has a widely unexplored potential that goes far beyond experimental quantum information science.

[1]  Mario Krenn,et al.  Active learning machine learns to create new quantum experiments , 2017, Proceedings of the National Academy of Sciences.

[2]  S. Barnett,et al.  Measuring the orbital angular momentum of a single photon. , 2002, Physical review letters.

[3]  Marco Barbieri,et al.  Simplifying quantum logic using higher-dimensional Hilbert spaces , 2009 .

[4]  Mario Krenn,et al.  Quantum Experiments and Graphs: Multiparty States as Coherent Superpositions of Perfect Matchings. , 2017, Physical review letters.

[5]  Tsuyoshi Murata,et al.  {m , 1934, ACML.

[6]  Mario Krenn,et al.  Path identity as a source of high-dimensional entanglement , 2020, Proceedings of the National Academy of Sciences.

[7]  Anthony Laing,et al.  Generation and sampling of quantum states of light in a silicon chip , 2018, Nature Physics.

[8]  Danna Zhou,et al.  d. , 1934, Microbial pathogenesis.

[9]  E. Knill,et al.  A scheme for efficient quantum computation with linear optics , 2001, Nature.

[10]  C. M. Natarajan,et al.  On-chip quantum interference between silicon photon-pair sources , 2013, Nature Photonics.

[11]  Robert Fickler,et al.  High-dimensional quantum gates using full-field spatial modes of photons , 2019, Optica.

[12]  Fabio Sciarrino,et al.  Integrated photonic quantum technologies , 2019, Nature Photonics.

[13]  Joseph M. Lukens,et al.  High-dimensional optical quantum logic in large operational spaces , 2018, npj Quantum Information.

[14]  Laura Mančinska,et al.  Multidimensional quantum entanglement with large-scale integrated optics , 2018, Science.

[15]  N. Spagnolo,et al.  Photonic quantum information processing: a review , 2018, Reports on progress in physics. Physical Society.

[16]  H. Weinfurter,et al.  Multiphoton entanglement and interferometry , 2003, 0805.2853.

[17]  B. Hiesmayr,et al.  Observation of Four-Photon Orbital Angular Momentum Entanglement. , 2015, Physical review letters.

[18]  Liang Jiang,et al.  New class of quantum error-correcting codes for a bosonic mode , 2016, 1602.00008.

[19]  D. Gottesman Fault-Tolerant Quantum Computation with Higher-Dimensional Systems , 1998, quant-ph/9802007.

[20]  Simone Atzeni,et al.  Integrated sources of entangled photons at telecom wavelength in femtosecond-laser-written circuits , 2017, 1710.09618.

[21]  Anton Zeilinger,et al.  Experimental access to higher-dimensional entangled quantum systems using integrated optics , 2015, 1502.06504.

[22]  Christine Silberhorn,et al.  On-chip generation of photon-triplet states. , 2016, Optics express.

[23]  R Raussendorf,et al.  A one-way quantum computer. , 2001, Physical review letters.

[24]  Andrew Forbes,et al.  Engineering two-photon high-dimensional states through quantum interference , 2016, Science Advances.

[25]  I. Chuang,et al.  Quantum Teleportation is a Universal Computational Primitive , 1999, quant-ph/9908010.

[26]  R. Nichols,et al.  A hybrid machine learning algorithm for designing quantum experiments , 2018, Quantum Machine Intelligence.

[28]  Guang-Can Guo,et al.  Arbitrary two-particle high-dimensional Bell-state measurement by auxiliary entanglement , 2019, Physical Review A.

[29]  Isaac L. Chuang,et al.  Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations , 1999, Nature.

[30]  Robert Fickler,et al.  Twisted photons: new quantum perspectives in high dimensions , 2017, Light: Science & Applications.

[31]  A. Zeilinger,et al.  Higher-order quantum entanglement , 1992 .

[32]  Mario Krenn,et al.  Experimental Greenberger–Horne–Zeilinger entanglement beyond qubits , 2018, Nature Photonics.

[33]  Mario Krenn,et al.  Advances in high-dimensional quantum entanglement , 2019, 1911.10006.

[34]  Barry C Sanders,et al.  Quantum gates on hybrid qudits , 2002 .

[35]  Barry C. Sanders,et al.  Experimental quantum cloning in a pseudo-unitary system , 2020 .

[36]  Graham D. Marshall,et al.  Large-scale silicon quantum photonics implementing arbitrary two-qubit processing , 2018, Nature Photonics.

[37]  Halina Rubinsztein-Dunlop,et al.  Roadmap on structured light , 2016 .

[38]  P. Xu,et al.  On-chip generation and manipulation of entangled photons based on reconfigurable lithium-niobate waveguide circuits. , 2014, Physical review letters.

[39]  David Poulin,et al.  Kitaev's Z_d-Codes Threshold Estimates , 2013, TQC.

[40]  Andrew Forbes,et al.  Simultaneous entanglement swapping of multiple orbital angular momentum states of light , 2016, Nature Communications.

[41]  Jian-Wei Pan,et al.  Quantum teleportation of multiple degrees of freedom of a single photon , 2015, Nature.

[42]  Hans-J. Briegel,et al.  Machine learning for long-distance quantum communication , 2019, PRX Quantum.

[43]  Roberto Morandotti,et al.  On-chip generation of high-dimensional entangled quantum states and their coherent control , 2017, Nature.

[44]  Mario Krenn,et al.  Quantum experiments and graphs. III. High-dimensional and multiparticle entanglement , 2018, Physical Review A.

[45]  Jian-Wei Pan,et al.  Quantum Teleportation in High Dimensions. , 2019, Physical review letters.

[46]  Philip Walther,et al.  Integrated-optics heralded controlled-NOT gate for polarization-encoded qubits , 2017, 1708.06778.

[47]  A. Zeilinger,et al.  High-Dimensional Single-Photon Quantum Gates: Concepts and Experiments. , 2017, Physical review letters.

[48]  Juan Miguel Arrazola,et al.  Machine learning method for state preparation and gate synthesis on photonic quantum computers , 2018, Quantum Science and Technology.

[49]  Reck,et al.  Experimental realization of any discrete unitary operator. , 1994, Physical review letters.

[50]  Barry C. Sanders,et al.  Randomized benchmarking for qudit Clifford gates , 2019, New Journal of Physics.

[51]  Jian-Wei Pan,et al.  Realization of a photonic controlled-NOT gate sufficient for quantum computation. , 2004, Physical Review Letters.

[52]  G. G. Stokes "J." , 1890, The New Yale Book of Quotations.

[53]  A. Zeilinger,et al.  Arbitrary d -dimensional Pauli X gates of a flying qudit , 2018, Physical Review A.

[54]  A. Zeilinger,et al.  Automated Search for new Quantum Experiments. , 2015, Physical review letters.

[55]  J. Preskill,et al.  Encoding a qubit in an oscillator , 2000, quant-ph/0008040.

[56]  E. Campbell,et al.  A quantum compiler for qudits of prime dimension greater than 3. , 2019, 1902.05634.

[57]  Mario Krenn,et al.  Entanglement by Path Identity. , 2016, Physical review letters.

[58]  Armin Tavakoli,et al.  Experimental quantum multiparty communication protocols , 2016, npj Quantum Information.

[59]  Martin Rötteler,et al.  Factoring with Qutrits: Shor's Algorithm on Ternary and Metaplectic Quantum Architectures , 2016, ArXiv.

[60]  Mario Krenn,et al.  Experimental High-Dimensional Entanglement by Path Identity , 2019, 1904.07851.

[61]  B. Sanders,et al.  Quantum encodings in spin systems and harmonic oscillators , 2001, quant-ph/0109066.

[62]  Jing Liu,et al.  A search algorithm for quantum state engineering andmetrology , 2016 .

[63]  A. Zeilinger,et al.  Multi-photon entanglement in high dimensions , 2015, Nature Photonics.